The "Thickness Generator " script requirements are the implicit definition of the original surface and it's definition domain. The thickness value can be defined not only as a constant (image 2 and 3) but also as a function evaluated over R^3: This can lead to very interesting new mathematical objects exploration.
The attached script is a modified version of the "Thickness generator" script in order to generate the object "PrettyBall", shown in the first attached image.
The second image show a fractal like result obtained by using a "gyroidal mixture" to fill the space of a thick gyroide ball...
MathMod script:

Hi,
The PrettyBall object is already formed by three separate objects.
I you want to export each one in a separate .obj file, the best way to do it is by erasing two components each time from the script, generate the last remaming object and then export as .obj file.
To erase two components from the script, you can use the button "Cut" in the "Model details" tabulation. This button erase the current component from the script and all it's dependencies so you don't have to deal with the script which can be confusing especially for big ones...
Hope this can help!_________________Cheers,
Abderrahman

Hi all,
In this second version of the "Thickness generator" script, we explore ways of applying some transformations (scaling, stretching and bending) to a given mathematical object.
We start with a cylinder filled with Gyroidal structure (third image), The first image shows the result of bending the cylinder to form a torus. The second image is the result of applying an helicoidal transformation to the cylinder.
The attached script is for the first image.
PS: When bending the cylinder to form the Torus, the Gyroidal structure at both extreme sides of the Y axis doesn't seem quite right as the remaining of the Torus...is there a way to eliminate this behavior, I mean, a better bending transformation than the : (x,y,z)--> (sqrt(x^2+y^2) - r2, y, z) ?
MathMod script:

Hi,
In K3DSurf the chain example with ":" can be converted to MathMod script by using multiples components separated by ",".
The MathMod way of visualizing many components is however more powerful than what you can find in K3DSurf because in MathMod, each component can have it's own definition domain, grid resolution or colors where in K3DSurf this is not possible.
Technically you can make K3DSurf visualize the PrettyBall object but you have to deal with many partial derivative functions. Also the result will not show up as good as with MathMod (limited grid resolution, unique coloring...)
Remember, K3DSurf is very good for showing unique mathematical object . MathMod is all about showing and managing multiples models in the same "scene"_________________Cheers,
Abderrahman

Hi,
Here it is the MathMod script for the chain example.
This script is not , however, the best one you can write for MathMod...why?
One way to make it more interesting is to change the domain definition of each components because every torus can be defined independently of the others: This will increase the resolution of your model without having to increase the grid. This is very useful thing because , for example, you can make interesting real time animation at low grid resolution

Hi all,
This is a twisted cube filled with the Schwarz-P structure.
The third image is the result of bending the cube to form a Torus...but still don't know what to do with the strange behavior at the extreme positions along the y axis! (the Schwarz-P structure seems to stretch more than it should be)
Working on it!
MathMod script: